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2009•arXiv (Cornell University)Open access

Note on (weak) Gorenstein global dimensions

Najib Mahdou, Mohammed Tamekkante

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Abstract

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein global dimension and we study the weak Gorenstein homological dimensions of direct product of rings, which gives examples of non-coherent rings of finite Gorenstein dimensions $>0$ and infinite classical weak dimension.

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What this paper is about

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein global dimension and we study the weak Gorenstein homological dimensions of direct product of rings, which gives examples of non-coherent rings of finite Gorenstein dimensions $>0$ and infinite classical weak dimension.

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Available abstract

In this note we characterize the (resp., weak) Gorenstein global dimension for an arbitrary ring. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein global dimension and we study the weak Gorenstein homological dimensions of direct product of rings, which gives examples of non-coherent rings of finite Gorenstein dimensions $>0$ and infinite classical weak dimension.

Key concepts: Hilbert's syzygy theorem, Global dimension, Dimension (graph theory), Mathematics, Pure mathematics, Product (mathematics), Geometry

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